Communications system using a sharply bandlimited keying waveform

ABSTRACT

This invention is a communication system utilizing sharply bandlimited waveforms for sampled data communications computed for each sample value in a sequence of data samples. The computed waveform is centered at a sample point, weighted by a corresponding data value, and truncated outside an appropriate time interval. Sampled digital data in a sequence of data samples is received by a computer and scaled according to the value r(t n ). A waveform generator, controlled by a computer, generates a sharply bandlimited keying waveform for each data sample and weights each waveform with the data and forms the sum of weighted waveforms to form the output signal in digital form which is converted to analog form. The analog output of the waveform generator is passed through a low-pass filter to filter out any harmonics generated, up-converted to produce a desired carrier frequency which can then be multiplexed, if required, and output as radio frequency (RF) energy which can be received by any standard receiver.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention in general describes a communications system, specifically a communications system having sharply bandlimited waveforms for sampled data communications.

2. Description of the Related Art

Proliferation of communications, radar, and other systems making use of electromagnetic wave propagation has resulted in overcrowding in the useful portions of the electromagnetic spectrum. Even line-of-sight communications links seldom utilize frequencies above the X-band because of the absorption and scattering by rain and other constituents of the troposphere. Consequently, it becomes more important for transmitters to radiate signals with well confined spectra so limited spectral space is used more efficiently.

In order to communicate a sequence of sampled digital data, r(t_(n)), over a band limited communications channel, the sequence of values must be transformed into an analog signal which is spectrally confined to the band available. Traditionally, confinement of radiated signals to assigned bands has been accomplished by frequency or phase modulation (FSK or PSK) followed by analog filtering operations at intermediate frequency and final amplifier stages of the transmitter. At the receiver, this signal is filtered from adjacent channels after appropriate down-conversion by utilizing analog filters to select the desired signal for subsequent conversion to digital form.

It is well known to those practicing the art that the spectrum of a signal formed from appropriate combinations of cardinal functions will have zero energy outside the designated frequency band width. For this to be exact, it is required that the cardinal functions be of infinite length. Theoretically, this causes no intersymbol interference since cardinal functions are zero at all sample points except one, t=0. Thus the analog/digital converter, appropriately synchronized and in the absence of noise, reads values of the transmitted sequence.

Functions of infinite length are not physically realizable. However, studies have shown that, by appropriately modifying the cardinal function, one can achieve excellent interpolation accuracies and resultant phase accuracies in direct sampling applications even if the function is truncated to just a few sample intervals.

In the field of electromagnetic transmission of digital data there is a need for an alternative to FSK and various forms of PSK signals which would improve the confinement of the signal spectrum to an assigned frequency band in transmitters and receivers. It is well known that bi-phase code modulation consists of a sequence of equal-length intervals, often called “chips”. Within each chip a sinusoid at the carrier frequency is bi-phase modulated; more specifically, the carrier phase within a chip is constant but may jump from chip-to-chip by 180 degrees in accordance with modulating binary data. A drawback to the application of this waveform is the 180° phase “jump” which causes spreading of its spectrum. However, after a bi-phase signal is modified by the process which is the subject of this invention, its spectrum is well-defined to the desired band.

Further, it is important that adjacent communication channel interference and mutual interference among radar, navigation, communications and other systems which depend upon electromagnetic radiation be prevented.

SUMMARY OF THE INVENTION

It is the object of this invention to transform a communications sequence in a communications system into an analog signal which is spectrally confined to the band available for the transmission within a band limited communications channel without compromising communication accuracy.

Another object of this invention is to improve spectral confinement thereby allowing closer channel spacing and better electromagnetic compatibility among radar, navigation, and communications systems.

These and other objects are achieved by a communication system using sharply bandlimited signals for sampled data communications wherein a sharply bandlimited waveform is computed for each sample value in a sequence of data samples. Each waveform is centered at a sample point, is weighted by the corresponding data value, and is truncated outside an appropriate time interval. Resulting data-weighted waveforms are summed in the computer for all data samples of the sequence to be communicated, and the result is converted to analog form, up-converted to the desired carrier frequency, and transmitted. Because the signal spectrum is sharply bandlimited, communication channels may be spaced more closely, permitting more channels in the same frequency band.

At the receiver, signal-plus-noise is down-converted, data is sampled and converted to digital form, de-multiplexed (if necessary), and delivered to corresponding users.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows the error for low-pass interpolation using cardinal functions and self-truncating cardinal functions for B/W=¾ and ½ (33% and 100% over-sampling, respectively) as a function of the truncation length as measured by N, the number of samples within the truncated interval.

FIG. 2a shows the output of the waveform generator, the sharply bandlimited keying waveform.

FIG. 2b shows the spectral confinement of the sharply bandlimited keying waveform.

FIG. 3 is a schematic of a transmission system utilizing a sharply bandlimited communications filter.

FIG. 4 depicts a test configuration for testing a sharply bandlimited communications system.

FIG. 5 shows (a) the measured spectrum of the output waveform of the waveform generator with interpolation and (b) the measured spectrum of the output waveform of the waveform generator without interpolation.

FIG. 6a shows the I component before processing.

FIG. 6b shows the Q component before processing.

FIG. 6c shows the I component after processing.

FIG. 6d shows the Q component after processing.

FIG. 6e shows the correlated magnitude (I²+Q²)^(½) of the I and Q components.

DESCRIPTION OF THE PREFERRED EMBODIMENT

In order to communicate a sequence of sampled digital data over a bandlimited communications channel in a format other than the conventional analog format, a bi-phase code modulation utilizing a sharply bandlimited keying waveform may used.

A sharply bandlimited keying waveform is computed for each sample value in a sequence of data samples and centered at a sample point, weighted by a corresponding data value, and truncated outside an appropriate time interval. For a predetermined carrier frequency, f_(o), it is well known in the art that sampling theory requires that the signal must be sampled at a rate f_(s)=4f_(o)/(2M−1) which is greater than or equal to twice the signal bandwidth, where M is an integer. Defining the bandwidth to be 1/t_(c), where t_(c) is the spacing between “chips” (elements of a phase code consisting of a sequence of equal-length intervals) or chip width, then the minimum sampling rate is f_(s)=2/t_(c).

A signal with no spectral energy outside the band from −W to +W is completely specified by samples taken at uniform intervals less than or equal to ½ W. The original signal may be exactly reconstructed from these sampled values, r(t_(n)), by the interpolation $\begin{matrix} {{r(t)} = {\sum\limits_{- \infty}^{+ \infty}\quad {{r\left( t_{n} \right)}{s\left( {t - t_{n}} \right)}}}} & (1) \end{matrix}$

where t_(n)=n/2W, n being the number of the samples, and the interpolation function, or sharply bandlimited keying waveform, sometimes called an interpolation waveform or sampling function, is $\begin{matrix} {{s(t)} = \frac{\left( {\sin \quad 2\pi \quad {Wt}} \right)}{\left( {2\pi \quad {Wt}} \right)}} & (2) \end{matrix}$

A bandpass signal with no spectral energy outside the bands −MW to −(M−1)W and (M−1)W to MW may also be completely specified by samples taken at ½ W (or shorter) intervals. The original function may be reconstructed exactly from these sampled values by the interpolation defined by Eq.(1).

Eq.(1) holds exactly only if s(t) as defined by Eq. (2) for the bandpass case is defined for all values of t from −∞ to +∞. The interpolation error (magnitude of the difference between right and left sides of Eq. (1)) grows as s(t) is truncated to shorter lengths, and as the width of the spectrum of the sampled signal, B, approaches ½ the sampling rate f_(s)+2W.

FIG. 1 shows the error for low-pass interpolation (Eqs. (1) and (2)) for B/W=¾ and ½ (33% and 100% over-sampling, respectively) as a function of the truncation length as measured by N, the number of samples within the truncated interval. FIG. 1 also shows how the interpolation error shrinks dramatically (for large N) as a self-truncating “taper” is applied to the interpolation function. This tapered function is given for the low-pass case where q=1−B/W and m depends on both q and N.

s(t)=[sin (2πqW/m)t/(2πqW/m)t] ^(m) sin 2πWt/2πWt   (3)

where q=1−B/W.

Since interpolation error is dramatically reduced using the “self-truncating” interpolation function, it is logically concluded that the spectrum of s(t) from Eq. (3) is better confined to the band −W to +W than of s(t) from Eq. (2). The same logic applies to the bandpass case since the taper of Eq. (3) (the bracketed factor raised to the power, m) may be used in the bandpass case with similar results.

The interpolation waveforms s(t) have the property that the zeros are at the right points so as not to cause intersymbol interference. An example of s(t) is plotted in FIG. 2a; the spectrum of s(t) is shown in FIG. 2b. Normally the keying waveform is truncated to a shorter time interval resulting in poor spectral confinement.

In the preferred embodiment, referring to FIG. 5, sampled digital data in a sequence of data samples 12, r(t_(n)) input to the system 10 where computer 14 and waveform generator 16 generate a weighted interpolation waveform r(t_(n))s(t−t_(n)) for each data sample 12. The sampled input data 12 can be voice, television signals, pagers, or any other signal sampled as a function of time.

The sequence of data-weighted waveforms is summed in a computer 14 for all data samples of the sequence to be communicated, and the result is converted to analog form by a digital-to-analog (D/A) converter (not shown), filtered in a low-pass filter 22, up-converted to the desired carrier frequency in up-converter 18, and the signal is transmitted by a conventional method for transmission of electromagnetic waves, a transmitter 24.

The computer 14 receives a data bit stream from the sampled input data 12 and performs three functions. First, the computer 14 controls a waveform generator 16, secondly it weighs each waveform with the data and, thirdly, it forms the sum of weighted waveforms in digital form. The waveform generator 16 takes the digital data bits form the output signal and converts it to analog form by the use of an internal digital-to-analog (D/A) converter (not shown). The mathematical mechanism by which a waveform generator 16 synthesizes the bandlimited signal is as described above.

The output of the waveform generator 16 (the sharply bandlimited keying waveform shown in FIG. 2a) is passed through an integral or external low-pass filter 22 which filters out any harmonics previously generated. The filtered output of the waveform generator 16 is applied to an up-converter where the signal is up-converted to the desired carrier frequency by way of intermediate frequency (IF) stage to the transmitter 24 for generation of a sampled data signal output as radio frequency (RF) energy. A number of data channels may be multiplexed consistent with the bandwidth, if desired, by the application of the filtered analog signal from the low-pass filter 22 to a multiplexer 21.

A number of data channels may be grouped as sub-bands and a digital-to-analog (D/A) converter (not shown) would convert the data to an analog form at a rate consistent with the group bandwidth. Final separation of data channels may then be accomplished by digital filtering.

At a receiving location, the transmitted signal, plus any induced noise, is preamplified by a low-noise amplifier 28, demultiplexed by a demultiplexer 28 and down-converted by a low-noise amplifier filter down-converter 32, data is sampled and converted to digital form by an analog-to-digital (A/D) converter 34 , separated into separate channels by a digital channel separation filter 36, and applied to an audio or digital display device 38.

In the formation and transmittal of the sharply bandlimited signals for sampled data communications, the waveform generator 16 receiving the sample data delivers accurate data to the receiver 28 unless the remainder of the transmitter 24 distorts the radiated waveform. The up-converter 18 and transmitter 24 power amplifier (not shown) must exhibit a flat amplitude and linear phase characteristic across the signal band. Since the signal is bandlimited, this is more easily accomplished by analog low-pass filters 22. The better spectral confinement achieved through the use of the device set forth above leads to closer channel spacing and better electromagnetic compatibility among radar, navigation, and communications channels.

Operational data interpolation computer 14 may be performed by a finite impulse response (FIR) filter (not shown) implemented by a digital signal processor (DSP) microchip, such as a Part no. DSP96002, manufactured by Motorola Corp. of Phoenix, Ariz. The preferred DSP should have a speed and digital precision to provide the same processing as computer 14, but requiring only a single microchip plus requisite drivers and power supplies. D/A conversion may also be performed by a much smaller unit than a waveform generator 16, such as a Model 1010-60-860, manufactured by KOR Industries of Garden Grove, Calif. digital-to-analog converter.

The better spectral confinement provided by this invention leads to closer channel spacing and better electromagnetic compatibility among radar, navigation, and communications systems.

FIG. 4 depicts a sharply bandlimited keying waveform test configuration 40 of the preferred embodiment under laboratory conditions to verify that the output data is identical to the input data prior to operational data link interpolation. See, Sharply Bandlimited Signals for Sampled Data Communications, NRL/MR/5330—94—7481, Jun 94, which is hereby incorporated by reference.

Directly sampled and digitized data 42 from a pseudo-random bi-phase coded sinusoid (not shown) are selected by a computer 43 and entered into a waveform generator 52 synthesizer memory module 44. These data are used to weight the interpolation function previously described incorporating the computer program set forth in Table 1. Table 1 specifies mathematically the mechanism by which the waveform generator synthesizes the bandlimited signal from a sequence of data signals. Samples 42 are taken from the sinusoid at intervals, t_(s), of 0.144 μs and have a width of biphase modulation chips, t_(c), equal to 0.288 μs. Weighted and summed interpolation functions are computed at 0.008 μs intervals corresponding to a 125 MHz rate of the first memory 44 of the waveform generator 52 and read into a fast digital-to-analog (D/A) converter 46.

Within the D/A converter 46, the digital values from first memory 44 are converted to analog form and low-pass filtered by a low-pass filter 48 (0 to 50 MHz) to form the bandlimited analog signal centered at f_(o) output of the waveform generator 52, FIG. 3. The waveform generator 52 in the test installation functioned not only as a waveform generator but also as a D/A converter 46 and a low-pass filter 48. The spectrum, as shown in FIG. 5a, of the bandlimited analog signal of the waveform generator 52 is measured by a spectrum analyzer 54. FIG. 5b shows the spectrum of the same phase coded signal but without the weighting of Eq. (3).

To analyze the performance of the sharply bandlimited keying waveform system (ie., to determine fidelity with the digital sample 42 from the bi-phase phase modulated sinusoid), the I and Q components 66 and 64, respectively, of the output from the waveform generator 52 with the measured spectrum from the spectrum analyzer 54 are split out in an I/Q detector 56 when a reference signal 58 is heterodyned against the signal having the sharply bandlimited keying waveform in phase quadrature in order to obtain phase and amplitude information. Phase accuracy, where the phase, φ, is defined as Tan⁻¹Q/I, is dependent upon careful matching of these separate quadrature channels. Accordingly, phase errors limit the performance achievable from subsequent digital processing.

The digital outputs of the A/D converters 66 and 68 are applied to a computer 74 where the I and Q components are correlated with the pseudo random code used to generate the original input data samples 42 in the correlator 76, and an envelope detector 78 computes the square root of the sum of the squares which is applied to a plotter 82 for display of the test data.

In the test configuration 40, the particular values of t_(s) and t_(c) were chosen to be integer multiples of the waveform generators 52 fast memory read interval of 0.008 μs. The cycle period of the output signal carrier frequency was also chosen to be an integer multiple of 0.008 μs (1/15.625=0.064 and 1/31.25=0.032). The results of this test are shown in FIG. 6a through 6 c. The curves in FIG. 6a and 6 b depicts I and Q components of the received signal; FIGS. 6c and 6 d show the I and Q components after correlator processing and FIG. 6e depicts the correlated magnitude (I²+Q²)^(½) from FIGS. 6c and 6 d.

It will be understood by those skilled in the art that still other variations and modifications are possible and can be affected without detracting from the scope of the invention as defined by the claims.

TABLE 1 10! RE-STORE “W_256BIPH1:,1400,1” 20 ! PROGRAM TO GENERATE A DIRECT SAMPLED MAXIMAL LENGTH BIPHASE WAVEFORM WITH WEIGHTED CHIPS 30 ! FOR OUTPUT TO THE HP8770 WAVEFORM SYNTHESIZER 40 PRINTER IS CRT 50 ! GENERATE MAXIMAL LENGTH SHIFT REGISTER SEQUENCE 60 OPTION BASE 1 70 SEPARATE ALPHA FROM GRAPHICS 80 GCLEAR 90 INTEGER X(8), Xs(255) 100 INTEGER I,J,K,N,Pn,Ix,Ic,Xn,Ns,Nz,Nc, Chip,Chs,Che 110 DIM F1$|60| 120 DIM Λa(25), La(25), Ra(25) 130 DIM W$|32767| 140 DIM Comm$|96| 141 GOTO 1250 150 Ix=67 !INITIAL CONDITION 160 N=8 !NUMBER OF STAGES 170 Ic=Ix 180 FOR I=N TO 1 STEP −1 ! SET INITIAL CONDITION 190  X(I)=0 200  Pn=2“(I−1) 210  IF Ic>=(Pn) THEN X(I)=1 220  IF Ic>=(Pn) THEN Ic=Ic−Pn 230 NEXT I 240 Pn=2“N−1 ! NUMBER OF ELEMENTS IN SEQUENCE 250 FOR I=1 TO Pn 260  Xn=(X(8)+X(4)+X(3)+X(2)) MOD 2! FEEDBACK CONNECTION 270  Xs(I)=X(8) 280  S=0 290  FOR K=1 TO N 300   S=S+X(K)*2“(K−1) 310  NEXT K 320  PRINT USING ““(D),3X,DDD”;X(8),X(7),X(6), X(5),X(4),X(3),X(2), X(1),S 330  FOR J=N TO 2 STEP −1 340   X(J)=X(J−1) 350  NEXT J 360  X(1)=Xn 370 NEXT I 380 RAD 390 DISP “ENTER CHIP WIDTH IN MICROSECONDS”; 400 INPUT Tc 410 DISP “ENTER THE CARRIER FREQUENCY”; 420 INPUT F 430 W=125. 440 ! DISP “ENTER THE SAMPLING RATE OF THE HP8770”; 450 ! INPUT W 400 DISP “ENTER NAME OF FILE WHERE DATA IS TO BE STORED”; 470 INPUT Nam$ 480 DISP “ ENTER A COMMENT DESCRIBING WAVEFORM”; 490 LINPUT Comm$ 500 Nc=T*W!NUMBER OF SAMPLES IN CHIP 510 Ns=Nc*Pn 520 Print “NUMBER OF SAMPLES IS ”;Ns 530 PRINT “LENGTH OF PULSE IS ”;Ns/W 540 Nz=(1−FRACT Ns/8))*8 550 PRINT Nz;“ ZEROS WILL BE ADDED TO MAKE SAMPLES A MULTIPLE OF 8” 560 Tp=(Nz+Ns)/W 570 PRINT “ TOTAL PULSE WILL BE ”;Tp 580 PRINT 590 PRINT “ +− 1 12-BIT WEIGHT” 600 VIEWPOINT 10,150,15,90 610 WINDOW 0,(Ns/w),−2048,2048 620 WINDOW 0,(Ns/W)/16,−1200,1200 630 FRAME 640 CLIP OFF 650 L=1 660 ! INTERPOLATION FUNCTION PARAMETERS 670 M1=13 ! FOR Λ .4 CHIP LENGTH !5 ! FOR Λ .144 CHIP LENGTH 680 M2=2 690 U=.1 700 Fo=F 710 Ws=2*Fo/(2*M1 −1) 720 Ic=0 721 Tw=Tc/2 722 Tw2=Tw/2 730 FOR T=0 TO (Ns/W) STEP 1/W ! STEP THROUGH THE ENTIRE PULSE 740  Chip=(T*W)/Nc+.5 750  Chs=Chip−5 760  Che=Chip+5 770 ! TAPER START AND END 780  IF Chip<=5 THEN Chs=5 790  IF Chip>=Pn−4 THEN Che=Pn−4 800  FOR N=Chs TO Che 801   FOR M−1 TO 2 810    Y=2*PI*Ws*(T−Tc*N−M*Tw+Tw2) 820    IF Y=0 THEN 830     S3=1 840     GOTO 910 850    ELSE 860     GOTO 880 870    END IF 880    S1=(SIN(M1*Y)−SIN((M1−1)*Y))/Y 890    S2=(SIN(U*Y)/(U*Y))“M2 900    S3=S1*S2 910    S1=((−1)“N)*(Xs(N)−.5)*2*S3 920    V=V+S4 921   NEXT M 930  NEXT N 940  ! LIMIT AMPLITUDE TO 1 V PEAK 950  V=V*.4 960  Mag=ABS(V) 970  IF Mag>=1 THEN V=V/Mag*.99 980  Ic=Ic+1 990  Z=INT(V*2047+.5) 1000  PLOT T,Z 1010  W$|L,L|=CHR$(BINAND(255,BINAND(Z,−256)/256)) 1020  W$|L+1,L+1|I=CHR$(BINAND(Z,255)) 1030  L=L+2 1040!PRINT USING “DDDDD,4X,DD.DDDD,4X,DDDDDD,4X, D.DDD”;I,X,Z,Y 1050  V=0 1060 NEXT T 1070 Nz=(1−FRACT(Ic/8)*8 1080 PRINT Nz;“ ZEROS WILL BE ADDED TO MAKE SAMPLES A MULTIPLE of 8” 1090 FOR I=1 TO Nz 1100  Ic=Ic+1 1110  W$|L,L|=CHR$(0) 1120  W$|L+1,L+1|=CHR$(0) 1130  L=L+2 1140 NEXT I 1150 PRINT “TOTAL SAMPLES=”;Ic 1160 B=0 1170 Cdir=0 1180 CREATE BDAT Nam$,1,L+200 1190 ASSIGN @Wf TO Nam$ 1200 OUTPUT @Wf;L−1,W$|I1,L−1|,Cdir,F,B,Tp,W,Comm$ 1210 ASSIGN @Wf TO * 1220! PRINT “=****** DONE *******” 1230! 1240! 1250! 1260! PROGRAM TO READ WAVEFORMS AND OUTPUT IN AN ARBITARY SEQUENCE 1270! CONVERTED TO SERIES 300 3/30/88 MOD 4/14/88 1280! PRINTER IS CRT 1290 GCLEAR 1300 CLEAR SCREEN 1310 PRINT “ PROGRAM TO SEND WAVEFORMS TO HP8770” 1320 PRINT 1330 PRINT “ AS A MINIMUM, FUNCTION KEYS 1 AND 2 NEED TO BE USED 1340 PRINT “ 1 TO LOAD WAVEFORMS FROM DISC AND STORE IN THE 8770 MEMORY” 1350 PRINT “ 2 TO SET UP THE SEQUENCING OF THE WAVEFORM DATA” 1360 PRINT 1370 PRINT “A MODE EXISTS VIA KEY 5 TO CHANGE TIME DELAY BY ENTRY OF TIME IN MICROSECONDS” 1380 ON KEY 1 LABEL “LOAD WAV” GOSUB 1480 1390 ON KEY 2 LABEL “SEQ SET” GOSUB 1820 1400 ON KEY 3 LABEL “SEQ CHG” GOSUB2180 1410 ON KEY 4 LABEL “STATUS” GOSUB 2030 1420 ON KEY 5 LABEL “DEL TIME” GOSUB 2250 1430 ON KEY 6 LABEL “CLOCK” GOSUB 2570 1440 ON KEY 7 LABEL “CAT” GOSUB 2690 1450 ON KEY 8 LABEL “RESTART” GOTO 1280 1460 KEY LABELS ON 1470 GOTO 1470 1480 F1$=“” 1490 OUTPUT 719;“*RST” 1500 OUTPUT 719;“PURGE BOTH” 1510 OUTPUT 719;“FORMAT SIGN” 1520 GOSUB 2570 !SELECT CLOCK SOURCE 1530 A=0 1540 S$=VAL$(A)! START FIRST WAVEFORM SEGMENT AND PACKET AT ZERO 1550 DISP “ENTER THE NUMBER OF WAVEFORM FILES”; 1560 INPUT J 1570 FOR I=1 TO J 1580  DISP “ENTER FILE NAME”; 1590  INPUT F$ 1600  F1$=F1$&F$&“*” 1610 NEXT I 1620 K=1 1630 PRINT “ WAVEFORM MEMORY CONTENTS” 1640 PRINT “ NAME LENGTH IN SAMPLES ADDRESS PULSE W at CLOCK BANDWIDTH START FREQ” 1650 FOR I=1 TO J 1660  M=POS(F1$|K|,“*”) 1670  F$=F1$|K,K+M−2| 1680  ASSIGN @W1 TO F$ 1690  K=K+M 1700  ENTER @W1,1;L,W$,Cdir,Fs,B,T,W,Comm$! READ NUMBER OF BYTES IN, AND DATA 1710  Nn(I)=L/2 1720  N$=VAL$(Nn(I))! NUMBER OF WAVE SEGMENTS 1730  PRINT USING “10A,4X,DDDDD,11X,DDDDD,6X,DDD.D, 4A,DDD,5X,DDD.DDD,6X,DD.DDD”;F$,Nn(I),Λ,T,” at “,W,B,Fs 1740  Λ1(I)=Λ 1750  U$|1,1|=CHR$(BINAND(255,BINAND(L,−256)/256)) 1760  U$|2,2|=CHRS$(BINAND(L,255)) 1770  OUTPUT 719;“WMEM “&S$&”,#Λ“z&U$&W$|1,L| 1780  Λ=Λ+Nn(I) 1790  S$=VAL$(Λ) NEXT START ADDRESS 1800 NEXT I 1810 RETURN 1820 DISP “ENTER NUMBER OF WAVEFORM SEGMENTS”; 1830 INPUT J2 1840 Y=1 1850 J1=J2 1860 FOR I=Y TO J1 1870  DISP “ENTER SEGMENT STARTING ADDRESS”; 1880  INPUT Aa(I) 1890  DISP “ENTER LENGTH OF SEGMENT”; 1900  INPUT La(I) 1910  DISP “ENTER NUMBER OF TIMES TO REPEAT SEGMENT”; 1920  INPUT Ra(I) 1930 NEXT I 1940 OUTPUT 719;“PURGE SEQ” 1950 FOR I=1 TO J2 1960  S$=VAL$(Λa(I)) 1970  N$=VAL$(La(I)) 1980  R$=VAL$(Ra(I)) 1990  OUTPUT 719;“PACLIT “&S$&”,“&N$&”,“&R$&”, AUTO” 2000 NEXT I 2010 OUTPUT 719;“GO” 2020 RETURN 2030 PRINT “ SEQUENCE STATUS” 2040 PRINT “ADDRESS LENGTH REPEATS TIME” 2050 FOR I=1 TO J2 2060  PRINT USING “DDDDD,3X,DDDDD,5X,DDDDD,4X, DDDD.DDD”;Λa(I),La(I),Ra(I),Ra(I)/F*LA(I) 2070 NEXT I 2080 PRINT “ WAVEFORM MEMORY CONTENTS” 2090 PRINT “ NAME LENGTH IN SAMPLES ADDRESS′ 2100 K=1 2110 FOR I=1 to J 2120  M=POS(F1$|K|,“*”) 2130  F$=F1$|K,K+M−2| 2140  K=K+M 2150  PRINT USING “10A,4X,DDDDD,12X,DDDDD,”;F$,Nn(I), Λ1(I) 2160 NEXT I 2170 RETURN 2180 CLEAR SCREEN 2190 GOSUB 2080 2200 DISP “TO CHANGE ONE SEGMENT ENTER SEGMENT NUMBER”; 2210 INPUT Y 2220 J1=Y 2230 GOTO 1860 2240 RETURN 2250!   GENERATING WAVEFORM SEQUENCES OF DESIRED TIME DURATION 2260 J2=J2+1 2270 PRINT “AT START THERE MUST BE ONLY ONE ZERO SEGMENT IN SEQUENCE” 2280 DISP “ENTER ADDRESS OF ZERO WAVEFORM SEGMENT”; 2290 INPUT Z 2300 DIPS “ENTER SEQUENCE POSITION OF ZEROS”; 2310 INPUT I2 2320 FOR I=J2 TO I2+2 STEP −1 2330  Λa(I)=Aa(I−1) 2340  La(I)=La(I−1) 2350  Ra(I)=Ra(I−1) 2360 NEXT I 2370 DISP “ENTER DESIRED TIME”; 2380 INPUT T 2390 IF T<6.1 THEN T=6.1 2400 L=INT(F/8+.5)*8! SEQUENCE MUST BE MULTIPLE OF 8 2410 R1=INT((T−3)/L*F)! REPETITIONS OF SEQUENCE L 2420 T2=T−R1*L/F 2430 L2=INT(T2*F/8+.5)*8 2440 R2=1 2450 Λa(I2)=Z 2460 La(I2)=L 2470 Ra(I2)=R1 2480 Λa(I2+1)=Z 2490 La(I2+1)=L2 2500 Ra(I2+1)=R2 2510 GOSUB 1940 2520 GOSUB 2030 2530 DISP “TO EXIT, ENTER AN E -- TO CONTINUE, ANTHING ELSE”; 2540 INPUT E$ 2550 IF E$=“E” THEN RETURN 2560 GOTO 2370 2570 ! ROUTINE TO MODIFY CLOCK SELECTION 2580 DISP “enter an EXT for external clock otherwise the internal 125MHz is assumed”; 2590 INPUT Cls$ 2600 IF Cls$=“EXT”THEN 2650 2610 F=125 2620 PRINT “INTERNAL CLOCK SELECTED FREQUENCY ASSUMED ”;F 2630 OUTPUT 719;“CLKSEL INT” 2640 RETURN 2650 F=120 2660 PRINT “EXTERNAL CLOCK SELECTED FREQUENCY ASSUMED ”;F 2670 OUTPUT 719;“CLKSEL EXT” 2680 RETURN 2690 ! GET A CATALOG OF DISC 2700 CAT 2710 RETURN 2720 END 

What is claimed is:
 1. A communications system comprising: means for generating a digital data sample; means for generating a sharply bandlimited keying waveform responsive to the digital data sample centered at a sample point; means for weighting the sharply bandlimited keying waveform by a corresponding data sample value and truncating outside an appropriate time interval; and means for transmitting the weighted sharply bandlimited keying waveform.
 2. A communications system, as in claim 1, wherein the means for generating an sharply bandlimited keying waveform for a data sample is a wave form generator.
 3. A method for transmitting a digital signal comprised of the steps of: sampling a first digital data signal to produce a digital data sample; generating a sharply bandlimited keying waveform for the digital data sample; weighting the sharply bandlimited keying waveform with a corresponding data sample value and truncating outside an appropriate time interval; converting the weighted sharply bandlimited keying waveform into an analog signal; and transmitting the analog signal. 